A010157 Continued fraction for sqrt(79).

8, 1, 7, 1, 16, 1, 7, 1, 16, 1, 7, 1, 16, 1, 7, 1, 16, 1, 7, 1, 16, 1, 7, 1, 16, 1, 7, 1, 16, 1, 7, 1, 16, 1, 7, 1, 16, 1, 7, 1, 16, 1, 7, 1, 16, 1, 7, 1, 16, 1, 7, 1, 16, 1, 7, 1, 16, 1, 7, 1, 16, 1, 7, 1, 16, 1, 7, 1, 16, 1, 7, 1, 16

Offset

0,1

Links

Harry J. Smith, Table of n, a(n) for n = 0..20000

G. Xiao, Contfrac.

Index entries for continued fractions for constants.

Index entries for linear recurrences with constant coefficients, signature (0,0,0,1).

Formula

From Amiram Eldar, Nov 13 2023: (Start)

Multiplicative with a(2) = 7, a(2^e) = 16 for e >= 2, and a(p^e) = 1 for an odd prime p.

Dirichlet g.f.: zeta(s) * (1 + 3/2^(s-1) + 9/4^s). (End)

Example

8.88819441731558885009144167... = 8 + 1/(1 + 1/(7 + 1/(1 + 1/(16 + ...)))). - Harry J. Smith, Jun 09 2009

Mathematica

ContinuedFraction[Sqrt[79], 300] (* Vladimir Joseph Stephan Orlovsky, Mar 09 2011 *)

Prog

(PARI) { allocatemem(932245000); default(realprecision, 23000); x=contfrac(sqrt(79)); for (n=0, 20000, write("b010157.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 09 2009

Crossrefs

Cf. A010531 (decimal expansion).

Sequence in context: A258146 A182551 A005486 * A244089 A195489 A245280

Adjacent sequences: A010154 A010155 A010156 * A010158 A010159 A010160

Keyword

nonn,cofr,easy,mult

Author

N. J. A. Sloane

Status

approved